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Anais da Academia Brasileira de Ciências

Print version ISSN 0001-3765On-line version ISSN 1678-2690

Abstract

LIMA, STÊNIO R.  and  CORDEIRO, GAUSS M.. The Extended Log-Logistic Distribution: Properties and Application. An. Acad. Bras. Ciênc. [online]. 2017, vol.89, n.1, pp.3-17. ISSN 0001-3765.  https://doi.org/10.1590/0001-3765201720150579.

We propose a new four-parameter lifetime model, called the extended log-logistic distribution, to generalize the two-parameter log-logistic model. The new model is quite flexible to analyze positive data. We provide some mathematical properties including explicit expressions for the ordinary and incomplete moments, probability weighted moments, mean deviations, quantile function and entropy measure. The estimation of the model parameters is performed by maximum likelihood using the BFGS algorithm. The flexibility of the new model is illustrated by means of an application to a real data set. We hope that the new distribution will serve as an alternative model to other useful distributions for modeling positive real data in many areas.

Keywords : exponentiated generalize; generating function; log-logistic distribution; maximum likelihood estimation; momen.

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